Sayfadaki görseller
PDF
ePub

be summed up under three heads: First. General development. Second. The acquirement in part of the methods, knowledge, habits and processes of routine engineering works; in other words, the learning of the trade element. Third. The cultivation of the habits, methods, and spirit of observation, investigation, design, and construction, which may be called professional training.

Technical education has become a recognized prerequisite to the proper practice of the engineering profession. While in the past so many of our ablest and most distinguished engineers have succeeded without this training, and in the future others having natures peculiarily fitted for the work and having secured a discipline not found in the schools, will succeed, yet present conditions are such that the man without this preparation is sadly handicapped, and this preparation is so necessary that it may be said to be a pre-requisite.

The value of an engineering education in the development of a youth is usually recognized. The discipline of the mind, the unfolding of the powers, the transformation from a boy to a man, is well accomplished by a technological course.

The trade-school element has not received much support from educators, but this kind of training has been demanded by many engineers. While the writer is not an advocate of "practical" education in the common acceptation of the term, and believes that the engineers who demand this do not properly appreciate the advantage of potentiality of growth, yet he believes that a working knowledge of engineering details and

methods may be wisely included in the instruction with no loss in discipline and development, and that it is due to employer and young graduate that a sufficient amount of this training be given to enable the latter to be of service from the start. While the first years of work must be an apprenticeship, the beginning must be too low down.

But, after all, the third object in an engineering education is the most important,-the special development, the cultivation of the spirit of investigation, invention, design, and construction, and the consideration of projects in a business-like and successful way. It should be the aim of schools of technology to arrange the curriculum and to carry on the instruction so that all these objects will be attained in such a proportion and with such an economy of time that the young engineer may advance farthest in his professional career in his first ten or twenty years.

What part, then, does mathematics have in these ideals? What subjects should be included and what length of time should be given in the instruction?

Mathematics has usually been considered to have a valuable disciplinary power. Judging from the results attained in the average student as ordinarily taught, it is probable that this value has been overestimated by educators.

The necessity for proper training in the use of mathematics as a part of the engineer's practice has not, it seems, been generally appreciated. The graduate should have such a knowledge and mastery of the elements and their use as to be a rapid and accurate

computer, thouroughly trustworthy in all ordinary computations and operations. This his employer has a right to demand at the start, though it is probable that this condition is not usually realized.

In the field of the higher professional work, the mathematical training is of inestimable value. The language of mathematics best expresses methods and results; its methods are short-cuts in applied science, labor-saving appliances in demonstration and design. The time was when the use of mathematics by the engineer was deprecated, and the college graduate was expected to forget all he knew upon taking up practical affairs, but now that these branches are taught and used as tools, they become indispensible in the training.

There is a further function as a pre-requisite for the proper presentation in the school of professional subjects whose treatment involves mathematical processes. In many cases, the use of mathematical terms and methods learned in these preliminary subjects, allows a much more rapid treatment, and in many studies they are essential to proper presentation, so that the mathematical training becomes an economical necessity. It is unnecessary to advance proof of this in a gathering of engineering instructors.

On the other hand, a prolonged study of the higher mathematics may be detrimental to the engineer's success. It may misdirect and misappropriate his efforts, and by fixing his mind on exact and theoretical conceptions, decrease his ability and distract his attention for judging indefinite data and from applying methods to every-day problems. For this reason and

because so many other subjects claim attention, the amount of time given to mathematics has been somewhat reduced in engineering courses.

It may be a question, then, as to what branches should be taught, and how extensive the training in mathematics should be. A consideration of the amount of pure mathematics given in the technological schools of the country will be of value. In Table I, below, the amount of time given to pure mathematics in twelve institutions, all having distinctively engineering courses of some reputation, with methods of instruction somewhat known to the writer, is shown.

TABLE I.

Data showing relation between time given to pure mathematics and that devoted to the entire course in twelve engineering schools:

[blocks in formation]
[blocks in formation]

2, 3, 4, 5,

C. E.

M. E.

1, 2, 3, 4,

(C. E.)

Purdue University......

University of California.

M. E.
(C. E.)
M. E.
C. E.
M. E.
C. E.

[blocks in formation]

1, 2, 3, 4,
2, 3, 4,
1, 2,
1, 2, 3,
1, 2, 3,
2, 3,
2, 3, 4,

1, 2, 3, 4, 5, 6, 7, 8, 9,
1, 2, 3, 4, 5, 6, 7, 8, 9,
1, 2, 3, 4, 5, 6, 7, 8, 9,
7, 8, 9,
5, 6, 7, 8, 9,
5, 6, 7, 8, 9,
5, 6, 7, 8, 9,
3, 4, 5, 6, 7, 8, 9,
4, 5, 7, 8, 9,
4, 5, 7, 8, 9, 10, 11,
4, 5, 6, 7, 8, 9,

5, 6, 7, 8, 9,

Total Number of Exercises.

Mathematics.
Per Cent, in

Mathematics.
Per Cent. in

Calculus.

Total in

2380

260 10.9 3.6 2328 290 12.5 5.2 2454 324 13.1 4.1 2920 356 12.2 3.3 2125 285 13.4 8.0 6. I 2556 360 14 1 3008 360 12.0 4.6 2844 300 10.5 4.2 3000 472 15.7 3.8 2339352 15.0 3.2 2339 501 21.1 3.2 2040 408 20.0 5.0

*. Arithmetic. 2. Algebra. 3. Plane Geometry. 4. Solid Geometry. 5. Plane Trigonometry. 6. Sperical Trigonometry. 7. Advanced Algebra. 8. Analytical Geometry. 9. Calculus. 10. Least Squares. 11. Differential Equations.

2807 337 11.8 5.1

It has not been feasible to consider all engineering schools, nor even all of the best, and several of the highest rank have been excluded because of a lack of knowledge of the time given to various subjects. The mathematical training in others does not vary far from those given in the table. Moreover, the table may not be strictly accurate, for the methods of counting and valuing time and the variety of methods of instruction make strict accuracy impossible. However, it is believed that the table is fairly representative of the relation of pure mathematics to the course of instruction in American engineering schools.

The investigation has included courses in civil engineering and mechanical engineering. The course in electrical engineering would show about the same requirements with, perhaps, a wider range of mathematics for work in advanced physics. The courses in mining engineering and in architecture would not vary far from those noted. Only the regular instruction in mathematics will be considered, since the amount given in connection with the technical instruction is so related to other instruction as to make accurate determination impossible.

The instruction in mathematics has been expressed as a percentage of the total number of exercises of the course. By this method much of the difference in value given to each exercise or recitation has been eliminated, and by means of it a fairer comparison may be made.

It will be seen by the table that there is a substantial agreement in the branches included, either as

« ÖncekiDevam »